A NUMERICAL-ANALYSIS OF TIME-DEPENDENT ISOLATED DENDRITIC GROWTH FOR CONDITIONS NEAR THE STEADY-STATE

A numerical model has been developed to model time dependent array growth. As a test for the model the spacing was made very large and the temperature gradient was reduced to zero so that results could be compared to approximate analytic solutions for an isolated dendrite. It was found that there was good agreement both for shape and for the composition field at steady state. Instead of finding a family of solutions as was expected a unique solution was found for a given bath undercooling. The steady state solution corresponded precisely to the value of a parameter σ* previously used to describe marginal stability. The condition was obeyed over many orders of magnitude change in the growth conditions. When the dendrite was perturbed by momentarily changing the bath undercooling the interface gradually returned to the steady state shape. It is suggested that the unique solution is the result of correctly including the surface energy and that the stability parameter could instead be considered to be the steady state growth parameter. © 1990.